Searching for text in the properties panel
Some of the way there.

Here is a script that looks at all the panel classes in the 'PROPERTIES' ui area.  Technically I've looked at all modules in bl_ui having a name beginning with "properties_".  Conveniently each of these modules will have a classes list. 

Alternateively could have looked for panel types in bpy.types and checked if the bl_space_type == 'PROPERTIES'

If the panel's label doesn't contain the word (lower case check) then it is unregistered


Result of running search on "collections"

import bpy
from importlib import import_module

def search_mark(self, context):
    layout = self.layout
    layout.label(text="FOUND", icon='INFO')

search_str = "mist"

import bl_ui
pmods = [m for m in dir(bl_ui) if m.startswith("properties_")]
for pm in pmods:
    mod = import_module("bl_ui.%s" % pm) 
    for cls in mod.classes:
        if cls.__name__.find("_PT_") == -1:
            continue
        if getattr(cls, "bl_label", "").lower().find(search_str) &gt; -1:
            cls.prepend(search_mark)
            print(cls.__name__, cls.bl_label)
        else:
            bpy.utils.unregister_class(cls)


the output searching for "mist"

EEVEE_WORLD_PT_mist Mist Pass


there is a mist pass panel, somewhere I have no idea where lol.

To UNDO this, type the following  command into python console

bpy.ops.script.reload()


to reinstate all panels.

Result on searching for "vertex"

DATA_PT_gpencil_vertexpanel Vertex Groups
DATA_PT_vertex_groups Vertex Groups   
DATA_PT_vertex_colors Vertex Colors
PARTICLE_PT_vertexgroups Vertex Groups


for these could grab the lhs of name, eg 'DATA' and for a properties space, set the context tab via 

space.context = 'DATA'


or via a py console example, will set one of the properties area's context to 'DATA'

&gt;&gt;&gt; for a in C.screen.areas:
...     if a.type == 'PROPERTIES':
...         break
...         
&gt;&gt;&gt; a.spaces.active.context = 'DATA'


Finally adding a panel with a search string input and a reload button would finish this off.  Apart from hacking the icons, I'm not aware of any method to highlight the tabs.